Calculate the final amount of an investment of R500 at a compound interest rate of 6% per annum for 2 years.

Steps to Solve

1. Convert the percentage rate to a decimal

To perform calculations with the interest rate, convert it from a percentage to a decimal by dividing by 100:

$r = \frac{6}{100} = 0.06$

2. Apply the compound interest formula

The formula for compound interest is:

$A = P(1 + r)^n$

Where: $A$ = the future value of the investment/loan, including interest $P$ = the principal investment amount (the initial deposit or loan amount) $r$ = the annual interest rate (as a decimal) $n$ = the number of years the money is invested or borrowed for

Plug in the given values: $P = 500$ $r = 0.06$ $n = 2$

$A = 500(1 + 0.06)^2$

3. Calculate the value inside the parentheses

$1 + 0.06 = 1.06$

So the equation becomes:

$A = 500(1.06)^2$

4. Calculate the exponent

$(1.06)^2 = 1.06 \times 1.06 = 1.1236$

Thus, the equation is now:

$A = 500 \times 1.1236$

5. Multiply to find the final amount

$A = 500 \times 1.1236 = 561.80$